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Acceleration Vector in Circular Motion

  1. Jan 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider a go-cart moving on a circular track of radius R = 40 m. Suppose it starts from rest and speeds up to 60 km/hr in 20 seconds, with a constant rate of increase of the speed.
    Calculate the magnitude of a.



    2. Relevant equations

    a(t) = a_t + α

    where the first term is the tangential acceleration and the second is the angular acceleration.


    3. The attempt at a solution

    I begin with the magnitude of a:

    mag of a = [(R^2)(α^2) - (R^2)(ω^4)]^.5

    Then I calculate ω:

    ω = v/R = (60000m/3600s)/40m = .4167 /s

    And I can calculate the tangential acceleration:

    a_t = Δv/Δt = (60000m/3600s)/20s = .8333 m/s^2

    Now I can calculate dω/dt = α:

    α = r*a_t = 40 m * .8333 m/s^2 = 33.33 /s^2

    Now to calculate the magnitude of the acceleration vector:

    mag of a = [(a_t)^2 + α^2]^.5 = 33.34 m/s^2

    But apparently this is wrong. Can anyone point out what I've missed? Seems pretty straightforward but I just can't get it.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 13, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Did you mean centripetal acceleration instead of angular one?

    This is wrong. the tangential acceleration is R times the angular acceleration a_t=αR.


    ehild
     
    Last edited: Jan 13, 2012
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